the main goal of the present paper is to extend classical results from the measure theory and dynamical systems to the fuzzy subset setting. in this paper, the notion of  dynamic equivalence relation is introduced and then it is proved that this relation is an equivalence relation. also, a new metric on the collection of all equivalence classes is introduced and it is proved that this metric is...

The first known continuous extension result was obtained by Lebesgue in 1907. In 1915, Tietze published his famous theorem generalising Lebesgue's from the plane to general metric spaces. He constructed an explicit formula involving distance function on space. Thereafter, several authors contributed other formulas. present paper, we show that all these constructions also preserve uniform contin...